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We solve the Dirichlet problem $\left.u\right|_{\mathbb{B}^n}=\varphi,$ forhyperbolic Poisson's equation $\Delta_h u=\mu$ where $\varphi\in L_1(\partial\mathbb{B}^n)$ and $\mu$ is a measure that satisfies a growth condition.  Next we present a short proof for Lipschitz continuity of solutions ofcertain hyperbolic Poisson's equations, previously established at\cite{ChenRas}.  In addition, we investigate some alternative assumptions on hyperbolicLaplacian, which are connected with Riesz's potential. Also, local H\"{o}ldercontinuity is proved for solution of certain hyperbolic Poisson's equations.  We show that, if $u$ is hyperbolic harmonic in the upper half-space, then$\frac{\partial u}{\partial y}(x_0,y)\to 0, y\to 0^+$, when boundary function$f$ of the functions $u$ is differentiable at the boundary point $x_0$. As acorollary, we show $C^1(\overline{\mathbb{H}^n})$ smoothness of a hyperbolicharmonic function, which is reproduced from the $C_c^1(\mathbb{R}^{n-1})$boundary values.

On Lipschitz continuity and smoothness up to the boundary of solutions of hyperbolic Poisson's equation